Singular perturbation methods for a class of initial and boundary value problems in multi-parameter classical digital control systems

A stable linear time-invariant classical digital control system with several widely different small coefficients multiplying the lowest functions is considered. It is formulated as a multi-parameter singularly perturbed system. Perturbation methods are developed for both initial and boundary value problems based on asymptotic expansions of the perturbation parameters. The approximate solution consists of an outer solution and a number of boundary layer correction solutions equal to the number of initial conditions lost in the process of degeneration. An example is provided for illustration.